CCSSM Standards for Mathematical Practice: Practice 4
Practice 4 discussed models in mathematics. Teachers play an important role in their students' development of knowing numbers and being able to represent them in multiple formats. The PLC Journal for grades K-2 discussed the opportunities to explore real-world problems and situations (Lasron, et. al., 2012b). Exploring these operations will allow students to solve and interpret these problems when represented mathematically. This connects to the NCTM Problem Standard of Problem Solving as well as Connections, because students will be able to make connections to real-world situations and solve problems given about the situation (NCTM, 2000). The article also pointed out that focusing students' attention on making sense out of the problem in order to ensure answers are reasonable is a must. If their answers are reasonable, it indicates students used key words from the problems correctly (Larson, et. al., 2012b). Students can use various forms to learn how to solve different types of problems, which reaches the NCTM Process Standard of Representations. Knowing how to represent a problem in different ways or knowing how to solve different problems a unique way will expand their perception of representing a problem (NCTM, 2000).
In the PLC Journal for grades 3-5, one important point made was about models not having to be simply hands-on manipulatives (Larson, et. al., 2012a). Models include symbols and tools such as graphs, formulas, diagrams, and tables. Another point the article made was that students need to determine whether or not the answer they got is reasonable. Reasoning and Proof, an NCTM Process Standard, fits here because students will decide if they have a reasonable answer based on their computations (Larson, et. al., 2012a). The teacher can support students when they check to see if their answer is correct. The branch of the NCTM Process Standards that this fits into is Communication. Students need to be able to articulate the way they expressed and computed their problem, and also analyze if the answer is reasonable (NCTM, 2000). Students may talk among each other to decide if the answer is reasonable or not. The teacher can make connections by facilitating classroom dialogue and making real world connections. In each video, the teacher facilitated discussion among the students. Some asked them to think quietly to themselves then turn and talk, while others did a project to practice using the models. Each classroom used different models. The younger students used manipulatives, and the classes gradually worked their way to using charts and tables as they accelerated in solving problems.
Larson, M. R., Fennell, F., Adams, T. L., Dixon, J. K., Kobett, B. M. & Wray, J. A. (2012a). Common core mathematics in a PLC at work: Grades 3-5. Bloomington IN: Solution Tree Press.
Larson, M. R., Fennell, F., Adams, T. L., Dixon, J. K., Kobett, B. M. & Wray, J. A. (2012b). Common core mathematics in a PLC at work: Grades K-2. Bloomington IN: Solution Tree Press.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston VA: National Council of Teachers of Mathematics
In the PLC Journal for grades 3-5, one important point made was about models not having to be simply hands-on manipulatives (Larson, et. al., 2012a). Models include symbols and tools such as graphs, formulas, diagrams, and tables. Another point the article made was that students need to determine whether or not the answer they got is reasonable. Reasoning and Proof, an NCTM Process Standard, fits here because students will decide if they have a reasonable answer based on their computations (Larson, et. al., 2012a). The teacher can support students when they check to see if their answer is correct. The branch of the NCTM Process Standards that this fits into is Communication. Students need to be able to articulate the way they expressed and computed their problem, and also analyze if the answer is reasonable (NCTM, 2000). Students may talk among each other to decide if the answer is reasonable or not. The teacher can make connections by facilitating classroom dialogue and making real world connections. In each video, the teacher facilitated discussion among the students. Some asked them to think quietly to themselves then turn and talk, while others did a project to practice using the models. Each classroom used different models. The younger students used manipulatives, and the classes gradually worked their way to using charts and tables as they accelerated in solving problems.
Larson, M. R., Fennell, F., Adams, T. L., Dixon, J. K., Kobett, B. M. & Wray, J. A. (2012a). Common core mathematics in a PLC at work: Grades 3-5. Bloomington IN: Solution Tree Press.
Larson, M. R., Fennell, F., Adams, T. L., Dixon, J. K., Kobett, B. M. & Wray, J. A. (2012b). Common core mathematics in a PLC at work: Grades K-2. Bloomington IN: Solution Tree Press.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston VA: National Council of Teachers of Mathematics
Good job. The various models is for solving problems. Remember that models can also be to set up situations, from which questions/problems may arise, not just model to find solutions. I am really glad that you picked up on other ways of modeling - because they arise very soon.
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